Mobile sensors can be used to effect complete coverage of a surveillance area for a given threat over time, thereby reducing the number of sensors necessary. The surveillance area may have a given threat profile as determined by the kind of threat, and accompanying meteorological, environmental, and human factors. In planning the movement of sensors, areas that are deemed higher threat should receive proportionately higher coverage. We propose a coverage algorithm for mobile sensors to achieve a coverage that will match—over the long term and as quantified by an RMSE metric—a given threat profile. Moreover, the algorithm has the following desirable properties: 1) stochastic, so that it is robust to contingencies and makes it hard for an adversary to anticipate the sensor's movement, 2) efficient, and 3) practical, by avoiding movement over inaccessible areas. Further to matching, we argue that a fairness measure of performance over the shorter time scale is also important. We show that the RMSE and fairness are, in general, antagonistic, and argue for the need of a combined measure of performance, which we call efficacy. We show how a pause time parameter of the coverage algorithm can be used to control the trade-off between the RMSE and fairness, and present an efficient offline algorithm to determine the optimal pause time maximizing the efficacy. Finally, we discuss the effects of multiple sensors, under both independent and coordinated operation. Extensive simulation results—under realistic coverage scenarios—are presented for performance evaluation.